My question to you is, in what ways can you share authority without making a total mishmash of your setting? I can certainly appreciate that DM's have a specific view of how their campaign should look and feel. How can you as a DM share responsibility, but not lose all authority?
I think in this case Hussar may have been getting at the point of "what responsibilities do you entrust to your players" rather than do you trust them to cheat or not to cheat. He can correct me of course, if I am wrong.
My personal theory of leadership and command (and control in a situation like this, as referee) is that implicit in the job of leadership and command is the responsibility to train and to shift obligation from a tightly controlled centralized authority to a more flexible and fluid style of multi-functional tactical capabilities that can operate from any point of command.
That means an organization, even a group of gamers, can shift more rapidly to successfully address any necessary pressure or demand presented by any anticipated, or even unforeseen obstacle or problem. (As an example I tell my wife all of the time, "It is not my job as husband and leader of this family to control all affairs of this household, it is my job to train everyone else so that if I'm not around or if I get killed, it will run just like, if not better, than if I was here." A commander doesn't control all things, he trains and then delegates. And the better the commander he is, the less he has to control.)
Therefore, if that is the case, and what Hussar was shooting at, I encourage my players to do the following kinds of things:
Devise their own orders of battle, march, communications and so forth.
Devise their own tactical and combat formations.
Keep their own records - they do not ask me "what so and so NPC said that time we met on the road to Gallipolis?" I say, "if you didn't write it down, then use your memory. I'm not your personal Wizard of Oz, and I don't think for you or tell you what you should or shouldn't know." Know it or don't, it's not my job to know it for you.
I let them keep up with their own character details like Armor class, ammunition counts, etc. They have to keep record and write it down, and I will occasionally check, but that is their job, not mine. I'm not a character policeman, I just regulate on rare occasion.
Mapping is their job. I do not map for them, show them maps, or remind them of how they have moved. If they get mapping guidance during the game then they find a map or draw their own.
Leadership - they arrange how the party operates and who is in it and what skills they need as a team and as individuals.
they handle their own leadership disputes and affairs.
We play with very flexible rules, but if there is a rules debate then somebody in the party is appointed "Look up Man." I hate rule-a-ramas, and I hate being the guy carrying around a bunch of textbooks. So I give that steamy pile of crap to them. I regulate violations, and interpret flexibilities, but I'm not a freaking lawyer, I'm a DM (a judge). So somebody in the party gets to be the lawyer, not me. Like it or not. Also I don't look up spells, powers, etc. they do and if necessary read them out loud so we all understand them.
Inventions and innovations - They are responsible for this. I will say this will work, or this will not as it is currently designed, or let's test this, but it is their invention and experiment, I just test it. This encourages innovation on their part. They want some advantage, they have to figure out what it is and how to make it work.
I encourage them to devise their own spells, capabilities, and skills. I encourage the players to use their own real world skills, such as tracking ability or survival skills or language skills and adopt them to their character in-game. If the player can speak Latin then so can their character. If the player can recognize a bear track then so can the character. If the player knows how to find water, so does the character.
Seek out their own experts and create their own networks. If they have an in-game question about who the last King of Syria was and what he did in Antioch then they go to a monk, an historian, a sage, or somebody else who knows. Not to me, I don't tell them. They do their own research, and they have learned over time to seek out more than one source of information just to make sure what they learn is accurate. Same with creating networks. Over time they have learned it is better to have a reliable, consistent network of people they can trust than to just go to a new stranger everytime they need something. But they have to build their own networks, it's not my job to make others interested in working with them. They do their own research, and discover their own answers, in and out of game.
Buy their own supplies and run their operation like a business. If they need something that is not available then they have to design it and get someone to build it for them and it may not be done right the first time it is tried. They don't tell me, "I need something that will do this, and who do I go to?" I say, "well then, you design it and build it, or you find someone who can. That's not my job."
I've found stuff like that takes a ton of work off me, inspires their creativity and innovation, encourages them to invent and design, and makes for a much more interesting milieu than if I invented everything. Because I simply cannot think of everything.
And besides my job as referee or game leader is not to control them but to guide them and then to turn them loose if possible. I give the mission parameters, but they have to make it happen. And they have to figure out how to make it happen.